%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU711^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:54 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 31
% Syntax : Number of formulae : 209 ( 67 unt; 0 typ; 27 def)
% Number of atoms : 1363 ( 271 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 1619 ( 186 ~; 281 |; 15 &; 877 @)
% ( 19 <=>; 162 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 46 usr; 37 con; 0-4 aty)
% ( 79 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 241 ( 0 sgn 146 !; 6 ?; 241 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
powersetI: $o ).
thf(func_def_4,type,
powersetE: $o ).
thf(func_def_5,type,
binunion: $i > $i > $i ).
thf(func_def_6,type,
binunionEcases: $o ).
thf(func_def_7,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
vIMP: $o > $o > $o ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
sF3: $o ).
thf(func_def_20,type,
sF4: $o ).
thf(func_def_22,type,
sF6: $o ).
thf(func_def_24,type,
sF8: $o ).
thf(func_def_25,type,
sF9: $o ).
thf(func_def_26,type,
sF10: $o ).
thf(func_def_29,type,
sK13: $o ).
thf(func_def_31,type,
sK15: $i > $i > $i ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) )
= powersetI ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(f2,axiom,
( powersetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(f3,axiom,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( ( in @ X2 @ X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) )
= binunionEcases ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(f4,conjecture,
( powersetI
=> ( powersetE
=> ( binunionEcases
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem) ).
thf(f5,negated_conjecture,
~ ( powersetI
=> ( powersetE
=> ( binunionEcases
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( in @ X0 @ ( powerset @ X1 ) ) )
= powersetI ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( powersetI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
! [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X3 ) )
=> ( ( ( in @ X0 @ X2 )
=> X1 )
=> ( ( ( in @ X0 @ X3 )
=> X1 )
=> X1 ) ) )
= binunionEcases ),
inference(rectify,[],[f3]) ).
thf(f9,plain,
( binunionEcases
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( ( in @ Y3 @ Y1 )
=> Y2 )
=> ( ( ( in @ Y3 @ Y0 )
=> Y2 )
=> Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ( powersetI
=> ( powersetE
=> ( binunionEcases
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f11,plain,
~ ( ( powersetI = $true )
=> ( ( powersetE = $true )
=> ( ( binunionEcases = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( powersetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f13,plain,
( powersetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( powerset @ Y2 ) )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
!= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionEcases = $true )
& ( powersetE = $true )
& ( powersetI = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f15,plain,
( ( binunionEcases = $true )
& ( powersetE = $true )
& ( powersetI = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
!= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
( ( binunionEcases = $true )
& ( powersetE = $true )
& ( powersetI = $true )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( $true
!= ( in @ ( binunion @ sK1 @ sK2 ) @ ( powerset @ sK0 ) ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f15]) ).
thf(f17,plain,
( binunionEcases
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( ( in @ Y3 @ Y1 )
=> Y2 )
=> ( ( ( in @ Y3 @ Y0 )
=> Y2 )
=> Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f18,plain,
( powersetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( powerset @ Y2 ) )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f19,plain,
( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f20,plain,
( $true
!= ( in @ ( binunion @ sK1 @ sK2 ) @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f21,plain,
( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f22,plain,
powersetI = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f23,plain,
powersetE = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f24,plain,
binunionEcases = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f25,plain,
( powersetI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f28,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( ( in @ Y3 @ Y1 )
=> Y2 )
=> ( ( ( in @ Y3 @ Y0 )
=> Y2 )
=> Y2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f17,f24]) ).
thf(f29,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( powerset @ Y2 ) )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f18,f23]) ).
thf(f30,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f25,f22]) ).
thf(f31,definition,
( sF3
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( ( in @ Y3 @ Y1 )
=> Y2 )
=> ( ( ( in @ Y3 @ Y0 )
=> Y2 )
=> Y2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f32,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( ( in @ Y3 @ Y1 )
=> Y2 )
=> ( ( ( in @ Y3 @ Y0 )
=> Y2 )
=> Y2 ) ) ) ) ) ) )
= sF3 ),
inference(reorient_equations,[],[f31]) ).
thf(f33,plain,
$true = sF3,
inference(definition_folding,[],[f28,f32]) ).
thf(f34,definition,
( sF4
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( powerset @ Y2 ) )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f35,plain,
$true = sF4,
inference(definition_folding,[],[f29,f34]) ).
thf(f36,definition,
( sF5
= ( powerset @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f37,plain,
( ( powerset @ sK0 )
= sF5 ),
inference(reorient_equations,[],[f36]) ).
thf(f38,definition,
( sF6
= ( in @ sK2 @ sF5 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f39,plain,
$true = sF6,
inference(definition_folding,[],[f21,f38,f37]) ).
thf(f40,definition,
( sF7
= ( binunion @ sK1 @ sK2 ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f41,plain,
( ( binunion @ sK1 @ sK2 )
= sF7 ),
inference(reorient_equations,[],[f40]) ).
thf(f42,definition,
( sF8
= ( in @ sF7 @ sF5 ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f43,plain,
( ( in @ sF7 @ sF5 )
= sF8 ),
inference(reorient_equations,[],[f42]) ).
thf(f44,plain,
$true != sF8,
inference(definition_folding,[],[f20,f43,f37,f41]) ).
thf(f45,definition,
( sF9
= ( in @ sK1 @ sF5 ) ),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
thf(f46,plain,
( ( in @ sK1 @ sF5 )
= sF9 ),
inference(reorient_equations,[],[f45]) ).
thf(f47,plain,
$true = sF9,
inference(definition_folding,[],[f19,f46,f37]) ).
thf(f48,definition,
( sF10
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
thf(f49,plain,
$true = sF10,
inference(definition_folding,[],[f30,f48]) ).
thf(f51,plain,
( ( ( in @ sF7 @ sF5 )
= $false )
| ( $true = sF8 ) ),
inference(iff_proxy_clausification,[],[f43]) ).
thf(f53,plain,
( ( $true
= ( in @ sK2 @ sF5 ) )
| ( sF6 = $false ) ),
inference(iff_proxy_clausification,[],[f38]) ).
thf(f54,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( ( in @ Y3 @ Y1 )
=> Y2 )
=> ( ( ( in @ Y3 @ Y0 )
=> Y2 )
=> Y2 ) ) ) ) ) ) ) )
| ( sF3 = $false ) ),
inference(iff_proxy_clausification,[],[f32]) ).
thf(f72,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( ( in @ Y3 @ Y1 )
=> Y2 )
=> ( ( ( in @ Y3 @ Y0 )
=> Y2 )
=> Y2 ) ) ) ) ) )
@ X1 )
= $true )
| ( sF3 = $false ) ),
inference(pi_proxy_clausification,[],[f54]) ).
thf(f73,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( binunion @ Y0 @ X1 ) )
=> ( ( ( in @ Y2 @ Y0 )
=> Y1 )
=> ( ( ( in @ Y2 @ X1 )
=> Y1 )
=> Y1 ) ) ) ) ) ) )
| ( sF3 = $false ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f74,plain,
! [X2: $i,X1: $i] :
( ( sF3 = $false )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( binunion @ Y0 @ X1 ) )
=> ( ( ( in @ Y2 @ Y0 )
=> Y1 )
=> ( ( ( in @ Y2 @ X1 )
=> Y1 )
=> Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f73]) ).
thf(f75,plain,
! [X2: $i,X1: $i] :
( ( sF3 = $false )
| ( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( binunion @ X2 @ X1 ) )
=> ( ( ( in @ Y1 @ X2 )
=> Y0 )
=> ( ( ( in @ Y1 @ X1 )
=> Y0 )
=> Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f76,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $true
= ( ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( binunion @ X2 @ X1 ) )
=> ( ( ( in @ Y1 @ X2 )
=> Y0 )
=> ( ( ( in @ Y1 @ X1 )
=> Y0 )
=> Y0 ) ) ) )
@ X3 ) )
| ( sF3 = $false ) ),
inference(pi_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binunion @ X2 @ X1 ) )
=> ( ( ( in @ Y0 @ X2 )
=> X3 )
=> ( ( ( in @ Y0 @ X1 )
=> X3 )
=> X3 ) ) ) ) )
| ( sF3 = $false ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X3: $o,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( binunion @ X2 @ X1 ) )
=> ( ( ( in @ Y0 @ X2 )
=> X3 )
=> ( ( ( in @ Y0 @ X1 )
=> X3 )
=> X3 ) ) )
@ X4 ) )
| ( sF3 = $false ) ),
inference(pi_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X3: $o,X1: $i,X4: $i] :
( ( $true
= ( ( in @ X4 @ ( binunion @ X2 @ X1 ) )
=> ( ( ( in @ X4 @ X2 )
=> X3 )
=> ( ( ( in @ X4 @ X1 )
=> X3 )
=> X3 ) ) ) )
| ( sF3 = $false ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X3: $o,X1: $i,X4: $i] :
( ( ( in @ X4 @ ( binunion @ X2 @ X1 ) )
= $false )
| ( sF3 = $false )
| ( $true
= ( ( ( in @ X4 @ X2 )
=> X3 )
=> ( ( ( in @ X4 @ X1 )
=> X3 )
=> X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X3: $o,X1: $i,X4: $i] :
( ( sF3 = $false )
| ( $true
= ( ( ( in @ X4 @ X1 )
=> X3 )
=> X3 ) )
| ( $false
= ( ( in @ X4 @ X2 )
=> X3 ) )
| ( ( in @ X4 @ ( binunion @ X2 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X3: $o,X1: $i,X4: $i] :
( ( ( ( in @ X4 @ X1 )
=> X3 )
= $false )
| ( sF3 = $false )
| ( $false
= ( ( in @ X4 @ X2 )
=> X3 ) )
| ( ( in @ X4 @ ( binunion @ X2 @ X1 ) )
= $false )
| ( $true = X3 ) ),
inference(imp_proxy_clausification,[],[f81]) ).
thf(f84,plain,
! [X2: $i,X3: $o,X1: $i,X4: $i] :
( ( $true = X3 )
| ( sF3 = $false )
| ( $true
= ( in @ X4 @ X1 ) )
| ( $false
= ( ( in @ X4 @ X2 )
=> X3 ) )
| ( ( in @ X4 @ ( binunion @ X2 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f82]) ).
thf(f86,plain,
! [X2: $i,X3: $o,X1: $i,X4: $i] :
( ( $true = X3 )
| ( $true
= ( in @ X4 @ X2 ) )
| ( sF3 = $false )
| ( ( in @ X4 @ ( binunion @ X2 @ X1 ) )
= $false )
| ( $true
= ( in @ X4 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f91,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) )
| ( sF10 = $false ) ),
inference(iff_proxy_clausification,[],[f48]) ).
thf(f92,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) )
@ X1 ) )
| ( sF10 = $false ) ),
inference(pi_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( in @ Y0 @ ( powerset @ X1 ) ) ) )
= $true )
| ( sF10 = $false ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( in @ Y0 @ ( powerset @ X1 ) ) )
@ X2 ) )
| ( sF10 = $false ) ),
inference(pi_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( sF10 = $false ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
= $false )
| ( sF10 = $false )
| ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X2: $i,X1: $i] :
( ( sF10 = $false )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ ( sK15 @ X1 @ X2 ) ) )
| ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f96]) ).
thf(f98,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( ( in @ ( sK15 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK15 @ X1 @ X2 ) @ X1 ) )
= $false )
| ( sF10 = $false ) ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f99,plain,
! [X2: $i,X1: $i] :
( ( sF10 = $false )
| ( ( in @ ( sK15 @ X1 @ X2 ) @ X1 )
= $false )
| ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f98]) ).
thf(f100,plain,
! [X2: $i,X1: $i] :
( ( sF10 = $false )
| ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( sK15 @ X1 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f98]) ).
thf(f110,plain,
( ( $true
= ( in @ sK1 @ sF5 ) )
| ( $false = sF9 ) ),
inference(iff_proxy_clausification,[],[f46]) ).
thf(f113,plain,
( ( sF4 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( powerset @ Y2 ) )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f34]) ).
thf(f114,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( powerset @ Y2 ) )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ Y2 ) ) ) ) )
@ X1 ) )
| ( sF4 = $false ) ),
inference(pi_proxy_clausification,[],[f113]) ).
thf(f115,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ Y1 ) ) ) ) ) )
| ( sF4 = $false ) ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f116,plain,
! [X2: $i,X1: $i] :
( ( sF4 = $false )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X1 @ Y1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( powerset @ Y0 ) )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ Y0 ) ) ) ) )
| ( sF4 = $false ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ ( powerset @ Y0 ) )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ Y0 ) ) )
@ X3 ) )
| ( sF4 = $false ) ),
inference(pi_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ ( powerset @ X3 ) )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X3 ) ) ) )
| ( sF4 = $false ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X3 ) ) )
| ( sF4 = $false )
| ( ( in @ X2 @ ( powerset @ X3 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X3 ) )
= $false )
| ( $true
= ( in @ X1 @ X3 ) )
| ( sF4 = $false )
| ( ( in @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f120]) ).
thf(f133,definition,
( spl21_1
<=> ( $true = sF8 ) ),
introduced(definition,[new_symbols(definition,[spl21_1])],[avatar_definition]) ).
thf(f134,plain,
( ( $true != sF8 )
| spl21_1 ),
inference(avatar_component_clause,[],[f133]) ).
thf(f137,definition,
( spl21_2
<=> ( ( in @ sF7 @ sF5 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl21_2])],[avatar_definition]) ).
thf(f139,plain,
( ( ( in @ sF7 @ sF5 )
= $false )
| ~ spl21_2 ),
inference(avatar_component_clause,[],[f137]) ).
thf(f140,plain,
( spl21_1
| spl21_2 ),
inference(avatar_split_clause,[],[f51,f137,f133]) ).
thf(f151,definition,
( spl21_5
<=> ( $true
= ( in @ sK2 @ sF5 ) ) ),
introduced(definition,[new_symbols(definition,[spl21_5])],[avatar_definition]) ).
thf(f153,plain,
( ( $true
= ( in @ sK2 @ sF5 ) )
| ~ spl21_5 ),
inference(avatar_component_clause,[],[f151]) ).
thf(f155,definition,
( spl21_6
<=> ( sF6 = $false ) ),
introduced(definition,[new_symbols(definition,[spl21_6])],[avatar_definition]) ).
thf(f157,plain,
( ( sF6 = $false )
| ~ spl21_6 ),
inference(avatar_component_clause,[],[f155]) ).
thf(f158,plain,
( spl21_5
| spl21_6 ),
inference(avatar_split_clause,[],[f53,f155,f151]) ).
thf(f164,definition,
( spl21_8
<=> ( $true = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl21_8])],[avatar_definition]) ).
thf(f166,plain,
( ( $true = sF6 )
| ~ spl21_8 ),
inference(avatar_component_clause,[],[f164]) ).
thf(f169,definition,
( spl21_9
<=> ( $true = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl21_9])],[avatar_definition]) ).
thf(f171,plain,
( ( $true = sF3 )
| ~ spl21_9 ),
inference(avatar_component_clause,[],[f169]) ).
thf(f197,definition,
( spl21_15
<=> ! [X2: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
| ( $true
= ( in @ X4 @ X1 ) )
| ( ( in @ X4 @ ( binunion @ X2 @ X1 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl21_15])],[avatar_definition]) ).
thf(f198,plain,
( ! [X2: $i,X1: $i,X4: $i] :
( ( ( in @ X4 @ ( binunion @ X2 @ X1 ) )
= $false )
| ( $true
= ( in @ X4 @ X1 ) )
| ( $true
= ( in @ X4 @ X2 ) ) )
| ~ spl21_15 ),
inference(avatar_component_clause,[],[f197]) ).
thf(f200,definition,
( spl21_16
<=> ! [X3: $o] : ( $true = X3 ) ),
introduced(definition,[new_symbols(definition,[spl21_16])],[avatar_definition]) ).
thf(f201,plain,
( ! [X3: $o] : ( $true = X3 )
| ~ spl21_16 ),
inference(avatar_component_clause,[],[f200]) ).
thf(f203,definition,
( spl21_17
<=> ( sF3 = $false ) ),
introduced(definition,[new_symbols(definition,[spl21_17])],[avatar_definition]) ).
thf(f205,plain,
( ( sF3 = $false )
| ~ spl21_17 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f206,plain,
( spl21_15
| spl21_16
| spl21_17 ),
inference(avatar_split_clause,[],[f86,f203,f200,f197]) ).
thf(f223,definition,
( spl21_22
<=> ! [X2: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( sK15 @ X1 @ X2 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl21_22])],[avatar_definition]) ).
thf(f224,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK15 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ~ spl21_22 ),
inference(avatar_component_clause,[],[f223]) ).
thf(f226,definition,
( spl21_23
<=> ( sF10 = $false ) ),
introduced(definition,[new_symbols(definition,[spl21_23])],[avatar_definition]) ).
thf(f228,plain,
( ( sF10 = $false )
| ~ spl21_23 ),
inference(avatar_component_clause,[],[f226]) ).
thf(f229,plain,
( spl21_22
| spl21_23 ),
inference(avatar_split_clause,[],[f100,f226,f223]) ).
thf(f231,definition,
( spl21_24
<=> ! [X2: $i,X1: $i] :
( ( ( in @ ( sK15 @ X1 @ X2 ) @ X1 )
= $false )
| ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl21_24])],[avatar_definition]) ).
thf(f232,plain,
( ! [X2: $i,X1: $i] :
( ( ( in @ ( sK15 @ X1 @ X2 ) @ X1 )
= $false )
| ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ~ spl21_24 ),
inference(avatar_component_clause,[],[f231]) ).
thf(f233,plain,
( spl21_24
| spl21_23 ),
inference(avatar_split_clause,[],[f99,f226,f231]) ).
thf(f238,definition,
( spl21_26
<=> ( $true = sF10 ) ),
introduced(definition,[new_symbols(definition,[spl21_26])],[avatar_definition]) ).
thf(f240,plain,
( ( $true = sF10 )
| ~ spl21_26 ),
inference(avatar_component_clause,[],[f238]) ).
thf(f248,definition,
( spl21_28
<=> ( $true = sF9 ) ),
introduced(definition,[new_symbols(definition,[spl21_28])],[avatar_definition]) ).
thf(f250,plain,
( ( $true = sF9 )
| ~ spl21_28 ),
inference(avatar_component_clause,[],[f248]) ).
thf(f257,definition,
( spl21_30
<=> ( $true
= ( in @ sK1 @ sF5 ) ) ),
introduced(definition,[new_symbols(definition,[spl21_30])],[avatar_definition]) ).
thf(f259,plain,
( ( $true
= ( in @ sK1 @ sF5 ) )
| ~ spl21_30 ),
inference(avatar_component_clause,[],[f257]) ).
thf(f261,definition,
( spl21_31
<=> ( $false = sF9 ) ),
introduced(definition,[new_symbols(definition,[spl21_31])],[avatar_definition]) ).
thf(f263,plain,
( ( $false = sF9 )
| ~ spl21_31 ),
inference(avatar_component_clause,[],[f261]) ).
thf(f264,plain,
( spl21_30
| spl21_31 ),
inference(avatar_split_clause,[],[f110,f261,f257]) ).
thf(f266,definition,
( spl21_32
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( in @ X2 @ ( powerset @ X3 ) )
= $false )
| ( ( in @ X1 @ X2 )
= $false )
| ( $true
= ( in @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl21_32])],[avatar_definition]) ).
thf(f267,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X3 ) )
= $false )
| ( ( in @ X1 @ X2 )
= $false )
| ( $true
= ( in @ X1 @ X3 ) ) )
| ~ spl21_32 ),
inference(avatar_component_clause,[],[f266]) ).
thf(f269,definition,
( spl21_33
<=> ( sF4 = $false ) ),
introduced(definition,[new_symbols(definition,[spl21_33])],[avatar_definition]) ).
thf(f271,plain,
( ( sF4 = $false )
| ~ spl21_33 ),
inference(avatar_component_clause,[],[f269]) ).
thf(f272,plain,
( spl21_32
| spl21_33 ),
inference(avatar_split_clause,[],[f121,f269,f266]) ).
thf(f274,definition,
( spl21_34
<=> ( $true = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl21_34])],[avatar_definition]) ).
thf(f276,plain,
( ( $true = sF4 )
| ~ spl21_34 ),
inference(avatar_component_clause,[],[f274]) ).
thf(f292,plain,
spl21_9,
inference(avatar_split_clause,[],[f33,f169]) ).
thf(f293,plain,
spl21_34,
inference(avatar_split_clause,[],[f35,f274]) ).
thf(f294,plain,
spl21_8,
inference(avatar_split_clause,[],[f39,f164]) ).
thf(f295,plain,
~ spl21_1,
inference(avatar_split_clause,[],[f44,f133]) ).
thf(f296,plain,
spl21_28,
inference(avatar_split_clause,[],[f47,f248]) ).
thf(f297,plain,
spl21_26,
inference(avatar_split_clause,[],[f49,f238]) ).
thf(f300,plain,
( ( $true = $false )
| ~ spl21_23
| ~ spl21_26 ),
inference(forward_demodulation,[],[f240,f228]) ).
thf(f301,plain,
( $false
| ~ spl21_23
| ~ spl21_26 ),
inference(trivial_inequality_removal,[],[f300]) ).
thf(f302,plain,
( ~ spl21_23
| ~ spl21_26 ),
inference(avatar_contradiction_clause,[],[f301]) ).
thf(f304,plain,
( ( $true = $false )
| ~ spl21_9
| ~ spl21_17 ),
inference(forward_demodulation,[],[f205,f171]) ).
thf(f305,plain,
( $false
| ~ spl21_9
| ~ spl21_17 ),
inference(trivial_inequality_removal,[],[f304]) ).
thf(f306,plain,
( ~ spl21_9
| ~ spl21_17 ),
inference(avatar_contradiction_clause,[],[f305]) ).
thf(f325,plain,
( ( $true = $false )
| ~ spl21_6
| ~ spl21_8 ),
inference(forward_demodulation,[],[f157,f166]) ).
thf(f326,plain,
( $false
| ~ spl21_6
| ~ spl21_8 ),
inference(trivial_inequality_removal,[],[f325]) ).
thf(f327,plain,
( ~ spl21_6
| ~ spl21_8 ),
inference(avatar_contradiction_clause,[],[f326]) ).
thf(f347,plain,
( ( $true = $false )
| ~ spl21_33
| ~ spl21_34 ),
inference(forward_demodulation,[],[f271,f276]) ).
thf(f348,plain,
( $false
| ~ spl21_33
| ~ spl21_34 ),
inference(trivial_inequality_removal,[],[f347]) ).
thf(f349,plain,
( ~ spl21_33
| ~ spl21_34 ),
inference(avatar_contradiction_clause,[],[f348]) ).
thf(f360,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ sK0 ) )
| ( $false
= ( in @ X0 @ sF5 ) )
| ( ( in @ X1 @ X0 )
= $false ) )
| ~ spl21_32 ),
inference(constrained_superposition,[],[f267,f37]) ).
thf(f376,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK15 @ sK0 @ X0 ) @ X1 ) )
| ( $true
= ( in @ X0 @ ( powerset @ sK0 ) ) )
| ( ( in @ X1 @ sF5 )
= $false ) )
| ~ spl21_24
| ~ spl21_32 ),
inference(constrained_superposition,[],[f360,f232]) ).
thf(f379,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ sF5 )
= $false )
| ( $true
= ( in @ X0 @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ ( sK15 @ sK0 @ X0 ) @ X1 ) ) )
| ~ spl21_24
| ~ spl21_32 ),
inference(trivial_inequality_removal,[],[f376]) ).
thf(f381,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK15 @ sK0 @ X0 ) @ X1 ) )
| ( ( in @ X1 @ sF5 )
= $false )
| ( $true
= ( in @ X0 @ sF5 ) ) )
| ~ spl21_24
| ~ spl21_32 ),
inference(forward_demodulation,[],[f379,f37]) ).
thf(f383,plain,
( ! [X0: $i] :
( ( $true
= ( in @ X0 @ sK2 ) )
| ( $true
= ( in @ X0 @ sK1 ) )
| ( ( in @ X0 @ sF7 )
= $false ) )
| ~ spl21_15 ),
inference(constrained_superposition,[],[f198,f41]) ).
thf(f397,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( in @ sK2 @ sF5 )
= $false )
| ( ( in @ ( sK15 @ sK0 @ X0 ) @ sF7 )
= $false )
| ( $true
= ( in @ X0 @ sF5 ) )
| ( $true
= ( in @ ( sK15 @ sK0 @ X0 ) @ sK1 ) ) )
| ~ spl21_15
| ~ spl21_24
| ~ spl21_32 ),
inference(constrained_superposition,[],[f381,f383]) ).
thf(f404,plain,
( ! [X0: $i] :
( ( $true
= ( in @ ( sK15 @ sK0 @ X0 ) @ sK1 ) )
| ( $true
= ( in @ X0 @ sF5 ) )
| ( ( in @ sK2 @ sF5 )
= $false )
| ( ( in @ ( sK15 @ sK0 @ X0 ) @ sF7 )
= $false ) )
| ~ spl21_15
| ~ spl21_24
| ~ spl21_32 ),
inference(trivial_inequality_removal,[],[f397]) ).
thf(f412,plain,
( ! [X0: $i] :
( ( ( in @ ( sK15 @ sK0 @ X0 ) @ sF7 )
= $false )
| ( $true
= ( in @ X0 @ sF5 ) )
| ( $true = $false )
| ( $true
= ( in @ ( sK15 @ sK0 @ X0 ) @ sK1 ) ) )
| ~ spl21_5
| ~ spl21_15
| ~ spl21_24
| ~ spl21_32 ),
inference(forward_demodulation,[],[f404,f153]) ).
thf(f413,plain,
( ! [X0: $i] :
( ( $true
= ( in @ ( sK15 @ sK0 @ X0 ) @ sK1 ) )
| ( ( in @ ( sK15 @ sK0 @ X0 ) @ sF7 )
= $false )
| ( $true
= ( in @ X0 @ sF5 ) ) )
| ~ spl21_5
| ~ spl21_15
| ~ spl21_24
| ~ spl21_32 ),
inference(trivial_inequality_removal,[],[f412]) ).
thf(f419,plain,
( ! [X0: $i] :
( ( $true
= ( in @ X0 @ sF5 ) )
| ( ( in @ ( sK15 @ sK0 @ X0 ) @ sF7 )
= $false )
| ( ( in @ sK1 @ sF5 )
= $false )
| ( $true = $false )
| ( $true
= ( in @ X0 @ sF5 ) ) )
| ~ spl21_5
| ~ spl21_15
| ~ spl21_24
| ~ spl21_32 ),
inference(constrained_superposition,[],[f381,f413]) ).
thf(f420,plain,
( ! [X0: $i] :
( ( $true
= ( in @ X0 @ sF5 ) )
| ( ( in @ sK1 @ sF5 )
= $false )
| ( $true = $false )
| ( ( in @ ( sK15 @ sK0 @ X0 ) @ sF7 )
= $false ) )
| ~ spl21_5
| ~ spl21_15
| ~ spl21_24
| ~ spl21_32 ),
inference(duplicate_literal_removal,[],[f419]) ).
thf(f421,plain,
( ! [X0: $i] :
( ( ( in @ sK1 @ sF5 )
= $false )
| ( $true
= ( in @ X0 @ sF5 ) )
| ( ( in @ ( sK15 @ sK0 @ X0 ) @ sF7 )
= $false ) )
| ~ spl21_5
| ~ spl21_15
| ~ spl21_24
| ~ spl21_32 ),
inference(trivial_inequality_removal,[],[f420]) ).
thf(f424,plain,
( ! [X0: $i] :
( ( $true
= ( in @ X0 @ sF5 ) )
| ( ( in @ ( sK15 @ sK0 @ X0 ) @ sF7 )
= $false )
| ( $true = $false ) )
| ~ spl21_5
| ~ spl21_15
| ~ spl21_24
| ~ spl21_30
| ~ spl21_32 ),
inference(forward_demodulation,[],[f421,f259]) ).
thf(f425,plain,
( ! [X0: $i] :
( ( ( in @ ( sK15 @ sK0 @ X0 ) @ sF7 )
= $false )
| ( $true
= ( in @ X0 @ sF5 ) ) )
| ~ spl21_5
| ~ spl21_15
| ~ spl21_24
| ~ spl21_30
| ~ spl21_32 ),
inference(trivial_inequality_removal,[],[f424]) ).
thf(f437,plain,
( ( $true
= ( in @ sF7 @ sF5 ) )
| ( $true = $false )
| ( $true
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ~ spl21_5
| ~ spl21_15
| ~ spl21_22
| ~ spl21_24
| ~ spl21_30
| ~ spl21_32 ),
inference(constrained_superposition,[],[f224,f425]) ).
thf(f439,plain,
( ( $true
= ( in @ sF7 @ sF5 ) )
| ( $true
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ~ spl21_5
| ~ spl21_15
| ~ spl21_22
| ~ spl21_24
| ~ spl21_30
| ~ spl21_32 ),
inference(trivial_inequality_removal,[],[f437]) ).
thf(f443,plain,
( ( $true
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ( $true = $false )
| ~ spl21_2
| ~ spl21_5
| ~ spl21_15
| ~ spl21_22
| ~ spl21_24
| ~ spl21_30
| ~ spl21_32 ),
inference(forward_demodulation,[],[f439,f139]) ).
thf(f444,plain,
( ( $true
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ~ spl21_2
| ~ spl21_5
| ~ spl21_15
| ~ spl21_22
| ~ spl21_24
| ~ spl21_30
| ~ spl21_32 ),
inference(trivial_inequality_removal,[],[f443]) ).
thf(f448,plain,
( ( $true
= ( in @ sF7 @ sF5 ) )
| ~ spl21_2
| ~ spl21_5
| ~ spl21_15
| ~ spl21_22
| ~ spl21_24
| ~ spl21_30
| ~ spl21_32 ),
inference(forward_demodulation,[],[f444,f37]) ).
thf(f449,plain,
( ( $true = $false )
| ~ spl21_2
| ~ spl21_5
| ~ spl21_15
| ~ spl21_22
| ~ spl21_24
| ~ spl21_30
| ~ spl21_32 ),
inference(forward_demodulation,[],[f448,f139]) ).
thf(f450,plain,
( $false
| ~ spl21_2
| ~ spl21_5
| ~ spl21_15
| ~ spl21_22
| ~ spl21_24
| ~ spl21_30
| ~ spl21_32 ),
inference(trivial_inequality_removal,[],[f449]) ).
thf(f451,plain,
( ~ spl21_2
| ~ spl21_5
| ~ spl21_15
| ~ spl21_22
| ~ spl21_24
| ~ spl21_30
| ~ spl21_32 ),
inference(avatar_contradiction_clause,[],[f450]) ).
thf(f464,plain,
( ( $true != $true )
| spl21_1
| ~ spl21_16 ),
inference(constrained_superposition,[],[f134,f201]) ).
thf(f475,plain,
( $false
| spl21_1
| ~ spl21_16 ),
inference(trivial_inequality_removal,[],[f464]) ).
thf(f476,plain,
( spl21_1
| ~ spl21_16 ),
inference(avatar_contradiction_clause,[],[f475]) ).
thf(f486,plain,
( ( $true = $false )
| ~ spl21_28
| ~ spl21_31 ),
inference(forward_demodulation,[],[f263,f250]) ).
thf(f487,plain,
( $false
| ~ spl21_28
| ~ spl21_31 ),
inference(trivial_inequality_removal,[],[f486]) ).
thf(f488,plain,
( ~ spl21_28
| ~ spl21_31 ),
inference(avatar_contradiction_clause,[],[f487]) ).
cnf(s1,plain,
( spl21_1
| spl21_2 ),
inference(sat_conversion,[],[f140]) ).
cnf(s3,plain,
( spl21_5
| spl21_6 ),
inference(sat_conversion,[],[f158]) ).
cnf(s9,plain,
( spl21_15
| spl21_16
| spl21_17 ),
inference(sat_conversion,[],[f206]) ).
cnf(s13,plain,
( spl21_22
| spl21_23 ),
inference(sat_conversion,[],[f229]) ).
cnf(s14,plain,
( spl21_23
| spl21_24 ),
inference(sat_conversion,[],[f233]) ).
cnf(s18,plain,
( spl21_30
| spl21_31 ),
inference(sat_conversion,[],[f264]) ).
cnf(s19,plain,
( spl21_32
| spl21_33 ),
inference(sat_conversion,[],[f272]) ).
cnf(s23,plain,
spl21_9,
inference(sat_conversion,[],[f292]) ).
cnf(s24,plain,
spl21_34,
inference(sat_conversion,[],[f293]) ).
cnf(s25,plain,
spl21_8,
inference(sat_conversion,[],[f294]) ).
cnf(s26,plain,
~ spl21_1,
inference(sat_conversion,[],[f295]) ).
cnf(s27,plain,
spl21_28,
inference(sat_conversion,[],[f296]) ).
cnf(s28,plain,
spl21_26,
inference(sat_conversion,[],[f297]) ).
cnf(s30,plain,
( ~ spl21_23
| ~ spl21_26 ),
inference(sat_conversion,[],[f302]) ).
cnf(s31,plain,
( ~ spl21_9
| ~ spl21_17 ),
inference(sat_conversion,[],[f306]) ).
cnf(s33,plain,
( ~ spl21_6
| ~ spl21_8 ),
inference(sat_conversion,[],[f327]) ).
cnf(s35,plain,
( ~ spl21_33
| ~ spl21_34 ),
inference(sat_conversion,[],[f349]) ).
cnf(s37,plain,
( ~ spl21_2
| ~ spl21_5
| ~ spl21_15
| ~ spl21_22
| ~ spl21_24
| ~ spl21_30
| ~ spl21_32 ),
inference(sat_conversion,[],[f451]) ).
cnf(s39,plain,
( spl21_1
| ~ spl21_16 ),
inference(sat_conversion,[],[f476]) ).
cnf(s41,plain,
( ~ spl21_28
| ~ spl21_31 ),
inference(sat_conversion,[],[f488]) ).
cnf(s42,plain,
~ spl21_23,
inference(rat,[],[s30,s28]) ).
cnf(s43,plain,
~ spl21_31,
inference(rat,[],[s41,s27]) ).
cnf(s44,plain,
~ spl21_16,
inference(rat,[],[s39,s26]) ).
cnf(s45,plain,
~ spl21_6,
inference(rat,[],[s33,s25]) ).
cnf(s46,plain,
~ spl21_33,
inference(rat,[],[s35,s24]) ).
cnf(s47,plain,
~ spl21_17,
inference(rat,[],[s31,s23]) ).
cnf(s48,plain,
spl21_32,
inference(rat,[],[s19,s46]) ).
cnf(s49,plain,
spl21_30,
inference(rat,[],[s18,s43]) ).
cnf(s50,plain,
spl21_24,
inference(rat,[],[s14,s42]) ).
cnf(s51,plain,
spl21_22,
inference(rat,[],[s13,s42]) ).
cnf(s52,plain,
spl21_15,
inference(rat,[],[s9,s47,s44]) ).
cnf(s53,plain,
spl21_5,
inference(rat,[],[s3,s45]) ).
cnf(s54,plain,
~ spl21_2,
inference(rat,[],[s37,s48,s49,s50,s51,s52,s53]) ).
cnf(s56,plain,
$false,
inference(rat,[],[s1,s54,s26]) ).
thf(f489,plain,
$false,
inference(avatar_sat_refutation,[],[s56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU711^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n006.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:13:09 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.30 % (781790)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.30 % (781798)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3570434418:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.23/0.30 % (781798)Refutation not found, incomplete strategy
% 0.23/0.30 % (781798)------------------------------
% 0.23/0.30 % (781798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (781798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (781798)CaDiCaL version: 2.1.3
% 0.23/0.30 % (781798)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.30 % (781798)Time elapsed: 0.004 s
% 0.23/0.30 % (781798)Peak memory usage: 12 MB
% 0.23/0.30 % (781798)Instructions burned: 11 (million)
% 0.23/0.30 % (781798)------------------------------
% 0.23/0.30 % (781798)------------------------------
% 0.23/0.30 % (781795)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1051716151:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.30 % (781796)lrs+10_16_si=on:nwc=1.5:random_seed=1298692269:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.30 % (781799)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1734420791:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.30 % (781797)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3999086816:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.30 % (781797)Refutation not found, incomplete strategy
% 0.23/0.30 % (781797)------------------------------
% 0.23/0.30 % (781797)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (781797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (781797)CaDiCaL version: 2.1.3
% 0.23/0.30 % (781797)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.30 % (781797)Time elapsed: 0.003 s
% 0.23/0.30 % (781797)Peak memory usage: 12 MB
% 0.23/0.30 % (781797)Instructions burned: 3 (million)
% 0.23/0.30 % (781801)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.30 % (781801)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.30 % (781803)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=835966891:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.30 % (781797)------------------------------
% 0.23/0.30 % (781797)------------------------------
% 0.23/0.30 % (781803)Instruction limit reached!
% 0.23/0.30 % (781803)------------------------------
% 0.23/0.30 % (781803)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (781803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (781803)CaDiCaL version: 2.1.3
% 0.23/0.30 % (781803)Termination reason: Instruction limit
% 0.23/0.30 % (781803)Termination phase: Saturation
% 0.23/0.30 % (781803)Time elapsed: 0.001 s
% 0.23/0.30 % (781803)Peak memory usage: 12 MB
% 0.23/0.30 % (781803)Instructions burned: 3 (million)
% 0.23/0.30 % (781796)Instruction limit reached!
% 0.23/0.30 % (781796)------------------------------
% 0.23/0.30 % (781796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (781796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (781796)CaDiCaL version: 2.1.3
% 0.23/0.30 % (781796)Termination reason: Instruction limit
% 0.23/0.30 % (781796)Termination phase: Saturation
% 0.23/0.30 % (781796)Time elapsed: 0.011 s
% 0.23/0.30 % (781796)Peak memory usage: 12 MB
% 0.23/0.30 % (781796)Instructions burned: 19 (million)
% 0.23/0.30 % (781801)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1888135041:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.30 % (781799)Instruction limit reached!
% 0.23/0.30 % (781799)------------------------------
% 0.23/0.30 % (781799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (781799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (781799)CaDiCaL version: 2.1.3
% 0.23/0.30 % (781799)Termination reason: Instruction limit
% 0.23/0.30 % (781799)Termination phase: Saturation
% 0.23/0.30 % (781799)Time elapsed: 0.013 s
% 0.23/0.30 % (781799)Peak memory usage: 12 MB
% 0.23/0.30 % (781799)Instructions burned: 25 (million)
% 0.23/0.30 % (781800)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2932737910:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.30 % (781801) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-781790-781801"...
% 0.23/0.30 % (781801)...printing done.
% 0.23/0.30 % (781801)Refutation found. Thanks to Tanya!
% 0.23/0.30 % SZS status Theorem for theBenchmark
% 0.23/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.31 % (781801)------------------------------
% 0.23/0.31 % (781801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (781801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (781801)CaDiCaL version: 2.1.3
% 0.23/0.31 % (781801)Termination reason: Refutation
% 0.23/0.31 % (781801)Time elapsed: 0.009 s
% 0.23/0.31 % (781801)Peak memory usage: 13 MB
% 0.23/0.31 % (781801)Instructions burned: 27 (million)
% 0.23/0.31 % (781790)Success in time 0.053 s
% 0.23/0.31 % Vampire exiting
%------------------------------------------------------------------------------